Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23761572 | C2 | semidirect |
| 135. C79 | #13600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773800 | 2 |
| #23765085 | 2 |
| #23761572 | 2 |
| C79×#2132 | 2 |
| #13600 | 79 |